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Entropy Definition and Formula

Entropy means the transformation of the state of the system by the change of thermal kinetic energy or heat per unit temperature which measure the amount of unavailable energy for doing useful work, entropy formula also uses to calculate the molecular disorder or chaotic motion (randomness) of a system in physical chemistry or physics. The concept of entropy obtained from the law of energy conservation in thermodynamics and unavailable energy in the Carnot cycle by the specific heat transfer. The higher the randomness greater will be the entropy for crystalline solids, gases, and liquid molecules. A system passes spontaneously from more orderliness to less orderliness. If the system is left to change its state spontaneously. Hence the system passes to the more chaotic state and the process of state change balancing when the system attains a maximum entropy values.

Entropy in 2nd Law of Thermodynamics

In learning chemistry or physics, for a spontaneous process, the entropy will be increasing and the process to attain equilibrium when the molecular disorder will attain maximum value. Therefore, the sum up of all entropy changes in the different parts of the system and the surrounding would rise. Hence, the second law tell us, the net entropy change of the universe are increasing for the irreversible process.

For example, if we lose a quantity of yellowish-green chlorine gas at the corner of the room. The gas density speared in all directions of the room until the equilibrium reached. Therefore, the state of equilibrium meaning a state of maximum disorder or entropy. Exactly a similar process happens when syrup gets diluted by diffusion in water added to it. Moreover, all the natural processes in our environment have a tendency to attain equilibrium by increasing the entropy of the system.

Clausius Definition of Entropy

The second law leads to the definition of the new property, called entropy. Like internal energy or enthalpy, entropy is a state function uses for understanding the condition of the system. Therefore, according to the Clausius definition, entropy equal to heat transfer that occurs reversibly by temperature change occurs in the system or ds = dqr/T. When heat change occurs in different temperatures, ds = dq1/T1 + dq2/T2 + dq3/T3 + … = ∫ dqr/T.

Work Done in Carnot Cycle

Entropy, thermodynamics formula uses to meaure transformation of state of system by change in heat or energy per unit temperature in Carnot cycle

French engineer Sadi Carnot (1824) study what quantity of work is obtainable from the heat in the Carnot engine. The typical Carnot engine consists of four successive operations. He takes the ideal gas which obeys ideal gas law in a cylinder fitted with a frictionless movable piston. The Carnot cycle operates in reversible paths. Let us take dq1 heat from HTR at T1 and rejected dq2 heat to LTR at T2. Now let us consider the quantity, heat change/temperature or entropy from the Carnot cycle diagram, for state A to C via B, heat change/ temperature = dq1/T1, and for state A to C via D, heat change/ temperature = dq2/T2.

But Carnot cycles states, dq1/T1 = dq2/T2. Therefore, we can conclude that heat change/temperature = constant for the change of two definite states of the gas molecule and independent of path change. From the whole cycles of operation, heat change/temperature, or net entropy is zero, and heat change /temperature define the fundamental thermodynamics property and a state function.

Unavailable Energy in Thermodynamics

From the Carnot cycles, dq1/T1 = dq2/T2. Where dq1 = energy supplied to the Carnot cycle at temperature T1. But the Carnot cycle fails to convert dq2 heat into useful work and rejected. The unavailable energy for the cycle = dq2. Hence the unavailable energy equation for Carnot cycle = temperature of the system × entropy increases due to energy take up.

Therefore, when a system absorbed a certain amount of heat in the reversible process. A part of absorbed energy can utilize for producing work, while the remaining part goes to increases the randomness of the molecule or increases the entropy of the system.